Question

what is the highest power of 91 that divides 78! ?

Answer 1

Answer:

6

91⁶ divides 78!

Step-by-step explanation:

what is the highest power of 91 that divides 78! ?

91 = 7 * 13

7 & 13 are co prime

78! = 78 * 77 * 76 *..............................................* 3 * 2 * 1

We will see the numbers from 1 to 78 which has 7 & 13 as factors

13 , 26 , 39 , 52 , 65 , 78   =   13⁶

7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70 , 77  = 7¹²  ( 49 = 7*7)

highest power of 91 that divides 78!  =  lower power out of 7 & 13

which is 6

=> 91⁶ divides 78!

Answer 2

Answer:

The highest power of 91 is 6 that divides 78!.

Step-by-step explanation:

We are given that 78!.

We have to find the highest power of 91 which divides 78!.

First we find the factor of 91 and then find the multiples of fcator of 91 in 78!.

Factors of 91

$91=13\times 7$

13 and 7 are the factors of 91

We find the mulitiples of 13 and 7 in 78!.

$78!=78\times77\times 77\times 76\times 75........3\times2\times 1$

Multiples of 7 in 78! are

7,14,21,28,35,42,49,56,63,70,77

Multiples of 13 in 78! are

13,26,39,52,65,78

Therefore, 13 are 6 times muliplies in 78! and 7 are 11 times multiples in 78!.

${13}^6\times 7^6={91}^6$.

Hence , the highest power of 91 is 6 that divides 78!.